You discover the sinister professor’s reason for using the population norms. He

Question

You discover the sinister professor’s reason for using the population norms. He was experimenting on his students without their knowledge: He gave them chocolates with drugs mixed into them. Since the drug he used was unsuccessful in affecting the class mean, he tries a new drug to improve scores. In a new class, i.e., your class, you get a drug might should affect test scores.

What is the null and alternative hypothesis? Be specific to the experiment. You can show mathematically or verbally. [assume one-tailed]

The class (n = 100) gets M = 62.25 (population data: µ = 60, = 15). He sets the alpha at .08, one tailed. What conclusion will he draw?  

Is the one-tailed test he selected more or less conservative than a two-tailed test? WHY?

What is the type I error rate of his study?

What would his alpha level of .08 compare to an alpha of .05 in terms of Type II error?

Explanation / Answer

The class (n = 100) gets M = 62.25 (population data: µ = 60, = 15). He sets the alpha at .08, one tailed. What conclusion will he draw?

Here, we have to use one sample z test for population mean. Given test is a one tailed test.

Z = (M - µ) / [/sqrt(n)]

Z = (62.25 – 60)/[15/sqrt(100)]

Z = 2.25/(15/10)

Z = 2.25/1.5

Z = 1.5

P-value = 0.0668

= 0.08

P-value <

So, reject the null hypothesis.

Is the one-tailed test he selected more or less conservative than a two-tailed test? WHY?

The selected one tailed test is less conservative than a two tailed test, because p-value for one tailed test is less than p-value for two tailed test.

What is the type I error rate of his study?

Type I error for this study is the probability of rejecting the null hypothesis that the average test score is 60, even it is not true.

What would his alpha level of .08 compare to an alpha of .05 in terms of Type II error?

If alpha level increases then type II error would be decrease because alpha value determines the limits of the data.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.